On the market viability under proportional transaction costs

Erhan Bayraktar, Xiang Yu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

2 Citations (Scopus)

Abstract

This paper studies the market viability with proportional transaction costs. Instead of requiring the existence of strictly consistent price systems as in the literature, we show that strictly consistent local martingale systems (SCLMS) can successfully serve as the dual elements such that the market viability can be verified. We introduce two weaker notions of no arbitrage conditions on market models named no unbounded profit with bounded risk (NUPBR) and no local arbitrage with bounded portfolios (NLABPs). In particular, we show that the NUPBR and NLABP conditions in the robust sense are equivalent to the existence of SCLMS for general market models. We also discuss the implications for the utility maximization problem.
Original languageEnglish
Pages (from-to)800-838
Number of pages39
JournalMathematical Finance
Volume28
Issue number3
DOIs
Publication statusPublished - 1 Jul 2018

Keywords

  • (robust) no local arbitrage with bounded portfolios
  • (robust) no unbounded profit with bounded risk
  • market viability
  • numéraire portfolios
  • proportional transaction costs
  • strictly consistent local martingale systems
  • utility maximization

ASJC Scopus subject areas

  • Accounting
  • Finance
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Applied Mathematics

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